Adaptive Wavelet Schwarz Methods for Nonlinear Elliptic Partial Differential Equations - Softcover

Lellek, Dominik

9783832540678: Adaptive Wavelet Schwarz Methods for Nonlinear Elliptic Partial Differential Equations

Softcover

ISBN 10: 3832540679 ISBN 13: 9783832540678

Publisher: Logos Verlag Berlin GmbH, 2015

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Adaptive wavelet methods have recently proven to be a very powerful instrument for the numerical treatment of nonlinear partial differential equations. In many cases, these methods can be shown to converge with an optimal rate with respect to the degrees of freedom and in linear complexity. In this thesis, we couple such algorithms with nonlinear Schwarz domain decomposition techniques. With this approach, we can develop efficient parallel adaptive wavelet Schwarz methods for a class of nonlinear problems and prove their convergence and optimality. We support the theoretical findings with instructive numerical experiments. In addition, we present how these techniques can be applied to the stationary, incompressible Navier-Stokes equation. Furthermore, we couple the adaptive wavelet Schwarz methods with a Newton-type method.

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